Pertanyaan

x → 0 lim 9 − 2 x − 9 − 4 x x + 4 − 3 x + 4 = ...

$x \to 0 lim \frac{x + 4 - 3 x + 4}{9 - 2 x - 9 - 4 x} =$ ...

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Ingat! Jika ada bentuk , maka: Sehingga:

Ingat!
Jika ada bentuk $begin mathsize 12px style limit as x rightwards arrow 0 of fraction numerator square root of a x plus b end root minus square root of c x plus d end root over denominator square root of p x plus q end root minus square root of r x plus s end root end fraction end style$ , maka:

$begin mathsize 12px style limit as x rightwards arrow 0 of fraction numerator square root of a x plus b end root minus square root of c x plus d end root over denominator square root of p x plus q end root minus square root of r x plus s end root end fraction equals limit as x rightwards arrow 0 of fraction numerator open square brackets open parentheses a x plus b right parenthesis minus left parenthesis c x plus d close parentheses close square brackets over denominator open square brackets open parentheses p x plus q right parenthesis minus left parenthesis r x plus s close parentheses close square brackets end fraction cross times fraction numerator square root of p x plus q end root plus square root of r x plus s end root over denominator square root of a x plus b end root plus square root of c x plus d end root end fraction end style$

Sehingga:

$begin mathsize 12px style limit as x rightwards arrow 0 of space fraction numerator square root of x plus 4 end root minus square root of 3 x plus 4 end root over denominator square root of 9 minus 2 x end root minus square root of 9 minus 4 x end root end fraction equals limit as x rightwards arrow 0 of space fraction numerator open parentheses x plus 4 close parentheses minus open parentheses 3 x plus 4 close parentheses over denominator open parentheses 9 minus 2 x close parentheses minus open parentheses 9 minus 4 x close parentheses end fraction cross times fraction numerator square root of 9 minus 2 x end root plus square root of 9 minus 4 x end root over denominator square root of x plus 4 end root plus square root of 3 x plus 4 end root end fraction equals limit as x rightwards arrow 0 of space fraction numerator negative up diagonal strike 2 x end strike over denominator up diagonal strike 2 x end strike end fraction cross times fraction numerator square root of 9 minus 2 x end root plus square root of 9 minus 4 x end root over denominator square root of x plus 4 end root plus square root of 3 x plus 4 end root end fraction equals limit as x rightwards arrow 0 of space left parenthesis negative 1 right parenthesis cross times fraction numerator square root of 9 minus 2 x end root plus square root of 9 minus 4 x end root over denominator square root of x plus 4 end root plus square root of 3 x plus 4 end root end fraction equals open parentheses negative 1 close parentheses cross times fraction numerator square root of 9 minus 2 open parentheses 0 close parentheses end root plus square root of 9 minus 4 open parentheses 0 close parentheses end root over denominator square root of open parentheses 0 close parentheses plus 4 end root plus square root of 3 open parentheses 0 close parentheses plus 4 end root end fraction equals open parentheses negative 1 close parentheses cross times 6 over 4 equals negative 3 over 2 end style$